Finite Group Databasebeta

← #29695357

Subgroups — #29695357

Order 15616.

1474 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840416C211yesmaximal, characteristic
2C2×#16839734C212yesmaximal, complemented
3#21448686C212yesmaximal, complemented
4#21446655C212yesmaximal, complemented
5#21446276C214yesmaximal, complemented
6#21445807C211yesmaximal, characteristic, complemented
7#21445735C212yesmaximal, complemented
8C4×#99×C61C211yesmaximal, characteristic, complemented
9C22×#11758224C2212yes—
10#16840416—22no—
11#16840416—24no—
12#16840416—22no—
13C2×#14519777C411yescharacteristic, complemented
14C2×#14519761C412yescomplemented
15C2×#14519761C2212yes—
16C2×#14519757C412yescomplemented
17C2×#14519751C411yescharacteristic, complemented
18C2×#14519751C2211yescharacteristic
19C2×C4×D244C411yescharacteristic, complemented
20C2×#14519733C2214yes—
21C22×C4⋊Dic61C411yescharacteristic, complemented
22C22×C4⋊Dic61C2211yescharacteristic
23#16839734—28no—
24C2×#14519692C2212yes—
25C2×#14519691C2214yes—
26C2×#14519691C2214yes—
27#16839660—22no—
28#16839647—24no—
29#16839623C2214yes—
30#16839622C2212yes—
31C4×C4⋊Dic61—22no—
32#16839529C2212yes—
33C2×C4×D4×C61C2211yescharacteristic
34C2×#99×C61C2211yescharacteristic
35C2×#99×C61C2211yescharacteristic
36C4×C22⋊C4×C61C2212yes—
37C61×#342C2212yes—
38C2×#11758224—24no—
39C2×#11758224—24no—
40C2×#11758224—24no—
41C2×#11758224—24no—
42C2×#11758224—44no—
43C22×Dic122C2×C412yes—
44C22×D244C2×C411yescharacteristic
45C22×C22⋊D61C2×C412yes—
46C22×C22⋊D61C2312yes—
47C23×Dic61C2×C412yes—
48C23×Dic61C2312yes—
49C22×C4×D61C2×C412yes—
50#14519777—22no—
51#14519777—22no—
52#14519761—24no—
53#14519761—24no—
54#14519761—24no—
55#14519761—24no—
56#14519757—24no—
57#14519757—24no—
58#14519751—22no—
59#14519751—22no—
60#14519751—22no—
61#14519751—22no—
62C4×D244—22no—
63C4×D244—21no—
64C4×D244—21no—
65#14519733—28no—
66#14519733—44no—
67C2×C4⋊Dic61—22no—
68C2×C4⋊Dic61—21no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61—22no—
71C2×C4⋊Dic61C2×C411yescharacteristic
72C2×C4⋊Dic61C2×C412yes—
73C2×C4⋊Dic61C2×C412yes—
74C2×C4⋊Dic61C2×C411yescharacteristic
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×C4⋊Dic61C2×C412yes—
77C2×C4⋊Dic61D412yes—
78C2×C4⋊Dic61D414yes—
79C2×C4⋊Dic61D412yes—
80C2×#11758196—24no—
81C2×C22⋊Dic61C2314yes—
82C2×#11758198C2×C412yes—
83C2×#11758198C2×C412yes—
84C2×#11758198C2×C412yes—
85C2×C4×Dic61—24no—
86#14519692—24no—
87#14519691—28no—
88#14519691—44no—
89#14519684—22no—
90#14519684—24no—
91#14519684—24no—
92C22×D4×C61C2311yescharacteristic
93C23×C4×C61C2×C411yescharacteristic
94C23×C4×C61C2311yescharacteristic
95C4×D4×C61—22no—
96C4×D4×C61—22no—
97C2×C4⋊C4×C61C2×C411yescharacteristic
98C2×C22⋊C4×C61C2×C411yescharacteristic
99C2×C22⋊C4×C61C2312yes—
100C2×C22⋊C4×C61C2311yescharacteristic
101C2×C22⋊C4×C61C2312yes—
102C2×C42×C61—22no—
103C2×C42×C61C2×C411yescharacteristic
104#99×C61—22no—
105#99×C61D414yescomplemented
106#95×C61—22no—
107C24×C61C22×C411yescharacteristic
108C24×C61C2411yescharacteristic
109C23×D61C22×C412yes—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61C2×D412yes—
113C2×D4×C61#4112yes—
114C22×C4×C61—22no—
115C22×C4×C61—21no—
116C22×C4×C61—21no—
117C22×C4×C61—22no—
118C22×C4×C61—42no—
119C22×C4×C61—42no—
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C2×D412yes—
126C22×C4×C61C2×D412yes—
127C2×C22⋊D61—24no—
128C2×C22⋊D61—22no—
129C2×C22⋊D61—24no—
130C2×C22⋊D61—22no—
131C2×C22⋊D61—24no—
132C2×C22⋊D61—24no—
133C2×C22⋊D61—42no—
134C22×Dic61—22no—
135C22×Dic61—22no—
136C22×Dic61—24no—
137C22×Dic61—24no—
138C22×Dic61—22no—
139C22×Dic61—22no—
140C22×Dic61—24no—
141C22×Dic61—42no—
142C22×Dic61C22×C412yes—
143C22×Dic61C22×C412yes—
144C22×Dic61C22×C412yes—
145C22×Dic61C2×D414yes—
146C22×Dic61C2×D414yes—
147#11758224—48no—
148#11758224—48no—
149#11758224—48no—
150#11758224—48no—
151C2×D244—21no—
152C2×D244—21no—
153C2×D244—42no—
154C2×C4×D61—24no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—42no—
158C2×Dic122—24no—
159C2×Dic122—24no—
160C2×Dic122—42no—
161C4⋊C4×C61—22no—
162C22⋊C4×C61—22no—
163C22⋊C4×C61—22no—
164C22⋊C4×C61—22no—
165C22⋊C4×C61—22no—
166C22⋊C4×C61—22no—
167C22⋊C4×C61C2×D414yes—
168C42×C61—21no—
169C42×C61—21no—
170C42×C61—44no—
171C22⋊Dic61—24no—
172C22⋊Dic61—24no—
173#11758198—24no—
174#11758198—22no—
175#11758198—22no—
176#11758198—24no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—22no—
180C4⋊Dic61—22no—
181C4⋊Dic61—24no—
182C4⋊Dic61—44no—
183C4⋊Dic61C22⋊C412yes—
184C4⋊Dic61C22⋊C411yescharacteristic
185C4⋊Dic61C22⋊C411yescharacteristic
186C4⋊Dic61C22⋊C412yes—
187C4⋊Dic61C22⋊C412yes—
188C4⋊Dic61C22⋊C414yes—
189C4⋊Dic61C22⋊C414yes—
190#11758196—48no—
191C4×Dic61—48no—
192C23×C61—21no—
193C23×C61—21no—
194C23×C61—41no—
195C23×C61—41no—
196C23×C61—41no—
197C23×C61—41no—
198C23×C61C4×D412yes—
199C23×C61C23×C411yescharacteristic
200C23×C61C22×D412yes—
201C23×C61C22×D411yescharacteristic
202C23×C61C2×#4111yescharacteristic
203C23×C61H(5,𝔽2)12yes—
204C22×D61—22no—
205C22×D61—22no—
206C22×D61—22no—
207C22×D61—42no—
208C22×D61—42no—
209D4×C61—24no—
210D4×C61—24no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—24no—
214C2×C4×C61—22no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—24no—
218C2×C4×C61—41no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—42no—
227C2×C4×C61—42no—
228C2×C4×C61—42no—
229C2×C4×C61C2×C22⋊C411yescharacteristic
230C2×C4×C61C2×C22⋊C412yes—
231C2×C4×C61C2×C22⋊C411yescharacteristic
232C2×C4×C61C4×D412yes—
233C22⋊D61—48no—
234C22⋊D61—44no—
235C22⋊D61—44no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—24no—
243C2×Dic61—24no—
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—44no—
248C2×Dic61—44no—
249C2×Dic61—44no—
250C2×Dic61—44no—
251C2×Dic61—44no—
252C2×Dic61C2×C22⋊C414yes—
253C2×Dic61C2×C22⋊C412yes—
254C2×Dic61C2×C22⋊C412yes—
255D244—42no—
256D244—42no—
257C4×D61—44no—
258C4×D61—44no—
259Dic122—48no—
260#22406—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—21no—
263C22×C61—22no—
264C22×C61—21no—
265C22×C61—22no—
266C22×C61—41no—
267C22×C61—41no—
268C22×C61—42no—
269C22×C61—42no—
270C22×C61—42no—
271C22×C61—41no—
272C22×C61—41no—
273C22×C61C22×C22⋊C411yescharacteristic
274C22×C61C2×C4×D411yescharacteristic
275C22×C61#51811yescharacteristic
276C22×C61D4212yes—
277C22×C61#54612yes—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61—42no—
281C2×D61—82no—
282C2×D61—82no—
283C4×C61—22no—
284C4×C61—21no—
285C4×C61—22no—
286C4×C61—44no—
287C4×C61—41no—
288C4×C61—41no—
289C4×C61—82no—
290C4×C61#41012yescomplemented
291Dic61—24no—
292Dic61—22no—
293Dic61—22no—
294Dic61—42no—
295Dic61—84no—
296C2×#547—611no—
297C2×#410—612no—
298#2344—612no—
299#1964—612no—
300#1899—614no—
301#1799—611no—
302#1782—612no—
303C4×#99D6111yescharacteristic, complemented
304C2×C61—22no—
305C2×C61—22no—
306C2×C61—21no—
307C2×C61—21no—
308C2×C61—42no—
309C2×C61D4×C22⋊C411yescharacteristic
310C2×C61C2×#41011yescharacteristic
311C2×C61#288411yescharacteristic
312D61—82no—
313C22×#41—612no—
314#547—1222no—
315#547—1224no—
316#547—1222no—
317C2×C4⋊Q8—611no—
318C2×#123—612no—
319C2×#123—612no—
320C2×C22⋊Q8—612no—
321C2×#121—611no—
322C2×#121—611no—
323C2×C4×D4—611no—
324C2×C4×D4C2×D6111yescharacteristic
325C2×#117—614no—
326C22×C4⋊C4—611no—
327C22×C4⋊C4—611no—
328#410—1228no—
329C2×#99—612no—
330C2×#99—614no—
331C2×#99—614no—
332C2×#99C2×D6111yescharacteristic
333C2×#99C2×D6111yescharacteristic
334#389—1222no—
335#387—1224no—
336#381—614no—
337#380—612no—
338C4×C4⋊C4—1222no—
339C4×C22⋊C4C2×D6112yes—
340#342—612no—
341#342C2×D6112yes—
342C61#2240611yescharacteristic, complemented, Sylow
343C2×#41—1224no—
344C2×#41—1224no—
345C2×#41—1224no—
346C2×#41—1224no—
347C2×#41—2444no—
348C22×Q8—612no—
349C22×D4—612no—
350C22×D4—612no—
351C22×D4—611no—
352C22×D4C22×D6111yescharacteristic
353C23×C4—612no—
354C23×C4—612no—
355C23×C4—612no—
356C23×C4C4×D6111yescharacteristic
357C23×C4C22×D6111yescharacteristic
358C4⋊Q8—1222no—
359C4⋊Q8—1222no—
360#123—1224no—
361#123—1224no—
362#123—1224no—
363#123—1224no—
364C22⋊Q8—1224no—
365C22⋊Q8—1224no—
366#121—1222no—
367#121—1222no—
368#121—1222no—
369#121—1222no—
370C4×D4—22no—
371C4×D4—22no—
372C4×D4—1222no—
373C4×D4—1221no—
374C4×D4—1221no—
375#117—1228no—
376#117—2444no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—612no—
380C2×C4⋊C4—612no—
381C2×C4⋊C4—614no—
382C2×C4⋊C4—612no—
383C2×C4⋊C4—611no—
384C2×C4⋊C4—612no—
385C2×C4⋊C4—612no—
386C2×C4⋊C4—1222no—
387C2×C4⋊C4—1221no—
388C2×C4⋊C4—1221no—
389C2×C4⋊C4—1224no—
390C2×C4⋊C4—1222no—
391C2×C4⋊C4C4×D6111yescharacteristic
392C2×C22⋊C4—612no—
393C2×C22⋊C4—612no—
394C2×C22⋊C4—612no—
395C2×C22⋊C4—614no—
396C2×C22⋊C4C4×D6111yescharacteristic
397C2×C22⋊C4C22×D6112yes—
398C2×C22⋊C4C22×D6111yescharacteristic
399C2×C22⋊C4C22×D6112yes—
400C2×C42—22no—
401C2×C42—1224no—
402C2×C42C4×D6111yescharacteristic
403#99—22no—
404#99—1224no—
405#99—1228no—
406#99—2444no—
407#99D24414yescomplemented
408#95—22no—
409#95—1224no—
410#95—1224no—
411#95—1222no—
412C24—612no—
413C24C2×C4×D6111yescharacteristic
414C24C23×D6111yescharacteristic
415#41—2448no—
416#41—2448no—
417#41—2448no—
418#41—2448no—
419C2×Q8—1224no—
420C2×Q8—1224no—
421C2×Q8—2442no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—1224no—
425C2×D4—1224no—
426C2×D4—1222no—
427C2×D4—1222no—
428C2×D4—1224no—
429C2×D4—1224no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—2442no—
433C2×D4—2442no—
434C2×D4C2×D24412yes—
435C2×D4#1175822212yes—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—42no—
441C22×C4—42no—
442C22×C4—612no—
443C22×C4—612no—
444C22×C4—614no—
445C22×C4—614no—
446C22×C4—612no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1222no—
452C22×C4—1222no—
453C22×C4—1224no—
454C22×C4—1224no—
455C22×C4—1224no—
456C22×C4—1224no—
457C22×C4—2442no—
458C22×C4—2442no—
459C22×C4C2×C4×D6111yescharacteristic
460C22×C4C2×C4×D6111yescharacteristic
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4C2×C4×D6111yescharacteristic
463C22×C4C2×C4×D6111yescharacteristic
464C22×C4D4×D6112yes—
465C22×C4D4×D6112yes—
466C4⋊C4—22no—
467C4⋊C4—612no—
468C4⋊C4—611no—
469C4⋊C4—611no—
470C4⋊C4—612no—
471C4⋊C4—612no—
472C4⋊C4—614no—
473C4⋊C4—614no—
474C4⋊C4—1222no—
475C4⋊C4—1222no—
476C4⋊C4—1224no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—2448no—
480C4⋊C4—2444no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—1222no—
487C22⋊C4—1222no—
488C22⋊C4—1224no—
489C22⋊C4—1224no—
490C22⋊C4—1224no—
491C22⋊C4—1224no—
492C22⋊C4C2×D24414yes—
493C42—21no—
494C42—21no—
495C42—44no—
496C42—2448no—
497C23—21no—
498C23—21no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—1222no—
504C23—1222no—
505C23—1222no—
506C23—2442no—
507C23—2442no—
508C23C4×D24412yes—
509C23C22×C4×D6111yescharacteristic
510C23C2×D4×D6112yes—
511C23C22×D24411yescharacteristic
512C23C2×#1175822211yescharacteristic
513C23#1451982312yes—
514Q8—2448no—
515D4—24no—
516D4—24no—
517D4—2442no—
518D4—2448no—
519D4—2444no—
520D4—2444no—
521D4—2442no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—612no—
541C2×C4—612no—
542C2×C4—614no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1224no—
548C2×C4—1224no—
549C2×C4—1224no—
550C2×C4—1224no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—2444no—
555C2×C4—2444no—
556C2×C4—2444no—
557C2×C4—2444no—
558C2×C4—2444no—
559C2×C4—2444no—
560C2×C4—2444no—
561C2×C4C22⋊C4×D6111yescharacteristic
562C2×C4C22⋊C4×D6112yes—
563C2×C4C22⋊C4×D6111yescharacteristic
564C2×C4C4×D24412yes—
565C22—22no—
566C22—21no—
567C22—22no—
568C22—21no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—41no—
576C22—41no—
577C22—4882no—
578C22—4882no—
579C22—2442no—
580C22—2442no—
581C22—2442no—
582C22C2×C22⋊C4×D6111yescharacteristic
583C22C2×C4×D24411yescharacteristic
584C22#1684023611yescharacteristic
585C22D4×D24412yes—
586C22#1684040812yes—
587C4—22no—
588C4—21no—
589C4—22no—
590C4—44no—
591C4—41no—
592C4—41no—
593C4—82no—
594C4—1222no—
595C4—1222no—
596C4—1224no—
597C4—4884no—
598C4—2442no—
599C4#1683973412yescomplemented
600C2—22no—
601C2—22no—
602C2—21no—
603C2—21no—
604C2—42no—
605C2—4882no—
606C2C22⋊C4×D24411yescharacteristic
607C2C2×#1683973411yescharacteristic
608C2#2145428111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC4×#99×C61C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840416C2
cosocleC24×C61C24
hypercenterC4×#99D61
hypocenterC61#22406
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#16839734C2semidirect
3. #21448686C2semidirect
4. #21446655C2semidirect
5. #21446276C2semidirect
6. #21445807C2semidirect
7. #21445735C2semidirect
8. C4×#99×C61C2semidirect
13. C2×#14519777C4semidirect
14. C2×#14519761C4semidirect
16. C2×#14519757C4semidirect
17. C2×#14519751C4semidirect
19. C2×C4×D244C4semidirect
21. C22×C4⋊Dic61C4semidirect
105. #99×C61D4semidirect
290. C4×C61#410semidirect
303. C4×#99D61semidirect
342. C61#22406semidirect
407. #99D244semidirect
599. C4#16839734semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168404162
C2×#168397342
#214486862
#214466552
#214462762
#214458072
#214457352
C4×#99×C612
#2240661